Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector

In this paper, we consider the application of the zero-order mini-batch optimization method in the problem of finding optimal control of a pencil of trajectories of nonlinear deterministic systems in the case of incomplete information about the state vector. The pencil of trajectories originates fro...

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Autores principales:	Andrei V. Panteleev, Aleksandr V. Lobanov
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	mini-batch algorithms metaheuristic optimal control satellite stabilization problem Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/4077332bc96441968cbb7abf4ef37547
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spelling	oai:doaj.org-article:4077332bc96441968cbb7abf4ef375472021-11-25T16:13:18ZApplication of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector10.3390/a141103321999-4893https://doaj.org/article/4077332bc96441968cbb7abf4ef375472021-11-01T00:00:00Zhttps://www.mdpi.com/1999-4893/14/11/332https://doaj.org/toc/1999-4893In this paper, we consider the application of the zero-order mini-batch optimization method in the problem of finding optimal control of a pencil of trajectories of nonlinear deterministic systems in the case of incomplete information about the state vector. The pencil of trajectories originates from a given set of initial states. To solve the problem, the structure of a feedback system is proposed, which contains models of the plant, measuring system, nonlinear state observer and control law of the fixed structure with unknown coefficients. The objective function proposed considers the quality of pencil of trajectories control, which is estimated by the average value of the Bolz functional over the given set of initial states. Unknown control laws of a plant and an observer are found in the form of expansions in terms of orthonormal systems of basis functions, which are specified on the set of possible states of a dynamical system. The original pencil of trajectories control problem is reduced to a global optimization problem, which is solved using the well-proven zero-order method, which uses a modified mini-batch approach in a random search procedure with adaptation. An algorithm for solving the problem is proposed. The satellite stabilization problem with incomplete information is solved.Andrei V. PanteleevAleksandr V. LobanovMDPI AGarticlemini-batch algorithmsmetaheuristicoptimal controlsatellite stabilization problemIndustrial engineering. Management engineeringT55.4-60.8Electronic computers. Computer scienceQA75.5-76.95ENAlgorithms, Vol 14, Iss 332, p 332 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	mini-batch algorithms metaheuristic optimal control satellite stabilization problem Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
spellingShingle	mini-batch algorithms metaheuristic optimal control satellite stabilization problem Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 Andrei V. Panteleev Aleksandr V. Lobanov Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector
description	In this paper, we consider the application of the zero-order mini-batch optimization method in the problem of finding optimal control of a pencil of trajectories of nonlinear deterministic systems in the case of incomplete information about the state vector. The pencil of trajectories originates from a given set of initial states. To solve the problem, the structure of a feedback system is proposed, which contains models of the plant, measuring system, nonlinear state observer and control law of the fixed structure with unknown coefficients. The objective function proposed considers the quality of pencil of trajectories control, which is estimated by the average value of the Bolz functional over the given set of initial states. Unknown control laws of a plant and an observer are found in the form of expansions in terms of orthonormal systems of basis functions, which are specified on the set of possible states of a dynamical system. The original pencil of trajectories control problem is reduced to a global optimization problem, which is solved using the well-proven zero-order method, which uses a modified mini-batch approach in a random search procedure with adaptation. An algorithm for solving the problem is proposed. The satellite stabilization problem with incomplete information is solved.
format	article
author	Andrei V. Panteleev Aleksandr V. Lobanov
author_facet	Andrei V. Panteleev Aleksandr V. Lobanov
author_sort	Andrei V. Panteleev
title	Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector
title_short	Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector
title_full	Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector
title_fullStr	Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector
title_full_unstemmed	Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector
title_sort	application of mini-batch metaheuristic algorithms in problems of optimization of deterministic systems with incomplete information about the state vector
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4077332bc96441968cbb7abf4ef37547
work_keys_str_mv	AT andreivpanteleev applicationofminibatchmetaheuristicalgorithmsinproblemsofoptimizationofdeterministicsystemswithincompleteinformationaboutthestatevector AT aleksandrvlobanov applicationofminibatchmetaheuristicalgorithmsinproblemsofoptimizationofdeterministicsystemswithincompleteinformationaboutthestatevector
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Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector

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